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2. A sociologist determines that a foreign-language student has learned
N1t2 20t t 2 vocabulary terms after t hours of uninterrupted study.
a. How many terms are learned between times t 2 and t 3?
b. What is the rate, in terms per hour, at which the student is learning at time
t 2?
c. What is the maximum rate, in terms per hour, at which the student is
learning?
3. A researcher found that the level of antacid in a person’s stomach, t minutes
6t
after a certain brand of antacid tablet is taken, is L1t2
t 2 . 2t 1
a. Determine the value of t for which L¿1t2 0.
b. Determine L1t2 for the value you found in part a.
c. Using your graphing calculator, graph L1t2.
d. From the graph, what can you predict about the level of antacid in a
person’s stomach after 1 min?
e. What is happening to the level of antacid in a person’s stomach from
2 t 8?
A
PART B
4. The operating cost, C, in dollars per hour, for an airplane cruising at a
height of h metres and an air speed of 200 km>
h is given by
C 4000 h 15 000 000
for the domain 1000 h 20 000. Determine
15 h
the height at which the operating cost is at a minimum, and find the operating
cost per hour at this height.
5. A rectangular piece of land is to be fenced using two kinds of fencing. Two
opposite sides will be fenced using standard fencing that costs $6>
m, while
the other two sides will require heavy-duty fencing that costs $9>
m. What are
the dimensions of the rectangular lot of greatest area that can be fenced for a
cost of $9000?
6. A real estate office manages 50 apartments in a downtown building. When
the rent is $900 per month, all the units are occupied. For every $25 increase
in rent, one unit becomes vacant. On average, all units require $75 in
maintenance and repairs each month. How much rent should the real estate
office charge to maximize profits?
7. A bus service carries 10 000 people daily between Ajax and Union Station,
and the company has space to serve up to 15 000 people per day. The cost to
ride the bus is $20. Market research shows that if the fare increases by
$0.50, 200 fewer people will ride the bus. What fare should be charged to
get the maximum revenue, given that the bus company must have at least
$130 000 in fares a day to cover operating costs?
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3.4 OPTIMIZATION PROBLEMS IN ECONOMICS AND SCIENCE
NEL